Question

Find the zeroes of each of the following polynomials and verify the relationship between its zeroes and coefficients. 4xsquare+5root2x-12

Answer 1

It is not a polynomials equation because 4xsquare then cubic form write it so that cubic form is not written do this equation is wrong

Answer 2

Answer:

Given:

•  Polynomial 4x² + 5√2x - 12

To find:

•  the zeroes of each of the following polynomials and

• verify the relationship between its zeroes and coefficients.

Pre-requisite Knowledge:

• Quadratic equation : $\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

If α and β are the zeros then,

• α + β = -b/a

• α * β = c/a

Solving Question:

  We are given the polynomial . thus we can find the zeros from that , then we could substitute the values in the above equation to find the answer.

Solution:

First to find the zeros

$a=4;b=5\sqrt{2};c=-12\\\\\implies \dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\\\\implies \dfrac{-5\sqrt{2} \pm \sqrt{50-16*(-12)}}{2*4}\\\\\\\\\implies \dfrac{-5\sqrt{2}\pm 11\sqrt{2}}{8}$

Thus, zeros are

⇒ (-5√2 + 11√2)/8

or, 6√2/8

or, 3√2/4

and

⇒ (-5√2 - 11√2 )/8

or, -16√2/8

or, -2√2

Then take this

If α and β are the zeros then,

α + β = -b/a

α * β = c/a

α =  3√2/4

β =  -2√2

α + β = 3√2/4 +   -2√2

or, (-8√2 + 3√2) / 4

or, -5√2/4 = -b/a = -5√2/4

α * β = c/a

α * β =  (3√2/4)*( -2√2 )

or, (3*√2*-√2)/2

or, -3*2/2

or, -3 = c/a = -12/4 = -3

∴ Verified